Achievement of a larger signal-to-error ratio, and thus of a larger dynamic range, for an FIR filter in a digital signal processing system such as a digital audio system, is required for an improved (audio) signal. The corresponding increases in the number of filter additions and multiplications, and increased quantization error will produce an increase in the noise “floor” that is present. This noise floor is often increased more for low frequencies than for higher frequencies (above 5 percent of sampling frequency).
K. C. Pohlmann, in Principles of Digital Audio, Howard W. Sams & Co., Indianapolis, Second Edition, 1989, pp. 121-123, discusses the possibility of noise (re)shaping through digital filtering, wherein the spectral shape for a noise curve is changed but the area under the noise curve is unchanged. Pohlmann appears to be more concerned about phase shifts associated with filtering than with other aspects of noise shaping.
What is needed is a supplemental approach that will lower the noise floor at the low frequency end relative to the high frequency end. Preferably, the approach should be capable of being applied independently of the upsampling process and at substantially any place in the overall filtering process. Preferably, the amount by which the low frequency noise floor is reduced should be controllable by a choice of one or more parameters used in the approach.